104 research outputs found
Theory of "Weak Value" and Quantum Mechanical Measurements
We review the definition and the concepts of the weak values and some
measurement model to extract the weak value. This material is based on the
author Ph.D. thesis "Time in Weak Values and Discrete Time Quantum Walk" at
Tokyo Institute of Technology (2011).Comment: to be published from "Measurements in Quantum Mechanics", edited by
M. R. Pahlavani (InTech, 2012) Chapter 4 page 75. Yutaka Shikano (2012).
ISBN: 978-953-51-0058-4 Available from:
http://www.intechopen.com/articles/show/title/theory-of-weak-value-and-quantum-mechanical-measuremen
From Discrete Time Quantum Walk to Continuous Time Quantum Walk in Limit Distribution
The discrete time quantum walk defined as a quantum-mechanical analogue of
the discrete time random walk have recently been attracted from various and
interdisciplinary fields. In this review, the weak limit theorem, that is, the
asymptotic behavior, of the one-dimensional discrete time quantum walk is
analytically shown. From the limit distribution of the discrete time quantum
walk, the discrete time quantum walk can be taken as the quantum dynamical
simulator of some physical systems.Comment: This is the invited review paper on the special issue on Theoretical
and Mathematical Aspects of Discrete Time Quantum Walk from Journal of
Computational and Theoretical Nanoscienc
Notes on Inhomogeneous Quantum Walks
We study a class of discrete-time quantum walks with inhomogeneous coins
defined in [Y. Shikano and H. Katsura, Phys. Rev. E {\bf 82}, 031122 (2010)].
We establish symmetry properties of the spectrum of the evolution operator,
which resembles the Hofstadter butterfly.Comment: 4 pages, 2 figures, as the proceedings of QCMC 201
Stereographical visualization of a polarization state using weak measurements with an optical-vortex beam
We propose a stereographical-visualization scheme for a polarization state by
two-dimensional imaging of a weak value with a single setup. The key idea is to
employ Laguerre-Gaussian modes or an optical vortex beam for a probe state in
weak measurement. Our scheme has the advantage that we can extract information
on the polarization state from the single image in which the zero-intensity
point of the optical vortex beam corresponds to a stereographic projection
point of the Poincare sphere. We experimentally perform single-setup weak
measurement to validate the stereographical relationship between the
polarization state on the Poincare sphere and the location of the
zero-intensity point.Comment: 6 pages, 4 figure
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